So this is a pretty vague question, and as such makes it difficult to provide a satisfying answer. The short answer is "yes" but there are a lot of subtle ways in which the question could be complicated. I can offer a few comments:
Yes, men had sex with men. However, the concept of homosexuality as an identity category did not really exist until closer to the 20th century. That is to say that men engaging in sex with other men during the mid 19th century would not have considered this central to their sense of self. Additionally, the category of "romantic friendship," which has no contemporary counterpart further complicates the issue. Romantic friendships were characterized by a strong romantic connection or interest, and might or might not contain a sexual element. So romantic expressions of love between men at the time of the Civil War were both common and socially acceptable.
However, I don't have anything to add in regards to the specific experience of same-sex intimacy and feeling amongst soldiers during the Civil War.